File managers usually list file sizes in binary GB. But storage devices are advertised in metric GB. So, your 4GB (metric) SD card is about 3.7GB (binary). It's a hardware limit, so there's really no way to increase the available space.
Recompression will save space, but reduce quality. There are utilities that'll batch process a ton of audio files. I used "dBpoweramp Music Converter" a couple times several years ago when I used Windows, I don't know if it's still any good.
If the bitrates vary widely among the files, ideally you'd start by reencoding the ones with the highest bitrate, since going from 320kbps to 128kbps will save more space than going from 160kbps to 128kbps.